Theresa May has refused to intervene in the case of Albert Thompson, the London cancer patient asked to pay £54,000 for treatment despite having lived in the UK for 44 years, as it emerged that there could be tens of thousands of people in a similarly uncertain immigration position.

Thompson, 63, is not receiving the radiotherapy treatment he needs for prostate cancer because he has been unable to provide officials with sufficient documentary evidence showing that he has lived in the UK continuously since arriving from Jamaica as a teenager in 1973. He is unable to pay the £54,000 fee.

May said responsibility for the decision to charge Thompson ahead of treatment lay with the Royal Marsden hospital. “No urgent treatment should ever be withheld or delayed by the NHS regardless of ability of willingness to pay,” she wrote in a letter to Jeremy Corbyn, who raised the issue at prime minister’s questions last week.

Regulations introduced last October require hospitals to check patients’ paperwork, including passports and proof of address, and charge upfront for their healthcare if they do not have documentary proof of eligibility, unless the treatment is deemed to be urgent. “The decision on whether his treatment is urgent or immediately necessary must rightly be made by the clinicians treating him,” May wrote.

The Royal Marsden has repeatedly said that Thompson’s radiotherapy was not urgent. This surprises some prostate cancer specialists, who are puzzled why treatment prescribed for cancer can subsequently be deemed non-urgent, once the question of ability to pay is raised.

Despite sympathising with “Mr Thompson and the worries he will be facing given his condition”, the prime minister said he needed to “evidence his settled status” in the UK.

Thompson – who has asked for his real name not to be used – is one of a growing group of long-term UK residents facing life-shattering problems as a result of the government’s hostile immigration environment, which has been particularly affecting people who arrived as children from Commonwealth countries.

Research released this week by academics at the University of Oxford-based Migration Observatory suggests that there could be up to 57,000 people potentially vulnerable to similar problems, because although they arrived from Commonwealth countries before 1971, they have never applied for a British passport or been naturalised. Their difficulties are only beginning to emerge now as the government’s tightened immigration regime inadvertently hits the wrong targets.

Madeleine Sumption, director of the Migration Observatory, said: “This is an estimate of the population who arrived before 1971 but have not naturalised. It won’t be the case that all 57,000 can’t prove their legal status; we don’t know what share of them have problems with their paperwork and what proportion have everything in order. This is the maximum size of the population who are potentially at risk.”

Thompson’s problems echo those experienced by Paulette Wilson, who was sent last year to an immigration detention centre and threatened with deportation to Jamaica, despite having been in Britain for 50 years. The Guardian has highlighted the cases of numerous other people who have lost their jobs or been made homeless because they are unable to prove they are in the UK legally, despite having lived in the country for over half a century.

Thompson’s lawyer Jeremy Bloom, at Duncan Lewis, said: “The application that Mr Thompson needs to make to regularise his stay is complex and requires a great deal of supporting evidence. Meanwhile, Mr Thompson is being refused potentially life-saving treatment unless he can pay for it. Theresa May does not appear to place much value on the contribution that Mr Thompson has made to the UK since 1973.”

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Labour’s Jonathan Ashworth, the shadow health secretary, highlighted news this week that the Royal Marsden foundation trust predicted it would receive an income of £210m over two years from providing private healthcare. “It’s astonishing that this man still hasn’t been able to access the treatment he needs. This is a trust which is making hundreds of millions from private patients, yet seemingly refusing to provide urgent cancer care,” he said.

A spokesperson for the the Royal Marsden said a cancer specialist would contact Thompson to discuss his treatment while he attempted to get his papers in order. Profits from private treatment were “ploughed back into the NHS for the benefit of our patients” and this had nothing to do with the the trust’s “legal obligation to check eligibility for access to NHS care”, the spokesperson said.

“It is disappointing that NHS staff, who are committed to public service, should be criticised for being professional and fair in applying the principles required of them on eligibility.”

Thompson, who worked as a mechanic and paid taxes for three decades before he became ill, has never applied for a British passport because he thought he had no need to; the Jamaican passport he arrived with was lost many years ago. He has also struggled to prove his eligibility for housing support and is currently living in a hostel. Over 87,000 people have signed a petition calling on the government to give him treatment.